On the order of approximation in limit theorems for Negative-Binomial sums of strictly stationary m-dependent random variables

Abstract

During the Iasi several decades, the results related to geometric random sums of independent identically distributed random variables have become interesting results in probability theory and in insurance, risk theory, queuing theory and stochastic finance, etc. The negative binomial random sums are extensions of geometric random sums. Up to the present, the negative binomial random sums of independent identically distributed random variables have attracted much attention since they appear in many fields. However, for die strictly stationary m-dependent summands, such negative-binomial random sums are rarely studied.